This is venturing into pure speculation, which is against the Rules of this forum. You've already been given an answer to your question, which is whether there is a branch of physics dealing with this.

Is there a branch of physics that exist over the speed of light? like a superphysics or hyperphysics?

There is no brance of physics for just FTL, because FTL is only known to be possible in Cosmology. (The study of the universe at a large scale) Galaxies beyond a certain distance from us reach recession velocities that are above c due to the metric expansion of space.

I assume this isn't anything like what you were expecting, but this is literally the only case of FTL that we know of.

If Brian is asking about the Hartman Effect involving virtual particles, or Cherenkov radiation resultant of a particle exceeding the phase velocity, but not the individual photonic speed, of light in a medium.
This might just be a matter of a terminology gap.

There was a paper published I want to say about a year ago (I looked but could not find it) that was somewhat along these lines. I could only get a little way through it because it was technical but the gist was that the paper was exploring what superluminal travel would be like according to GR/SR-type theories; acknowledging that such travel was by all accounts impossible.